Now that we have a procedure to map \(\hat{H_{s}}\)  from the eigenstates of \(\hat{H}_{el}\) , it remains to address the question of how to determine the latter. Electronic structure methods have evolved during the years in order to address this point and have now reached a very high degree of sophistication and accuracy. Wave function based methods, such as complete active space, are among the most popular methods to implement Eq. REF , as they directly provide \(E_{k}\)  and \(| k\rangle \)[1]}, [2]}. Density functional theory can also be used to determine spin Hamiltonian coefficients but within a different mapping formalism from the one presented here. DFT's solutions cannot in fact be easily interpreted as electronic excited states with a well defined \(S^{2}\)  value and a different expression from Eq. REF  is thus necessary. An extensive review of electronic structure and spin Hamiltonian mapping is beyond the scope of this work and we redirect the interested reader to the rich literature on this field.[3]}, [1]}, [5]}, [2]}
